In general relativity, unstable closed geodesics arise naturally in the study of the linear wave evolution on the background of both Schwarzschild and Kerr black holes.
A substantial amount of work has accumulated around this topic, see for example the early works by Blue and Soffer, see [1]} as well the very recent
study of Price's law by Hintz [2]}.
The latter paper was preceded by the work of Tataru [3]}, as well as the results by Donninger, Soffer and the author [4]} on the spatially local, but temporally global, decay of linear waves on Schwarzschild. Metcalfe, Tataru, and Tohaneanu [5]} subsequently established Price’s law on nonstationary spacetimes with sufficient decay in a suitable sense. We now set out to describe the author's results in more detail.
